The Tai Chi of Basic Mathematics
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- Kelley O’Neal’
- 7 years ago
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1 In 1960, I was an SMSG (School Study Group) product, and mathematics enlightened me. Although we re no longer racing to the moon, maybe it is time to reflect on the direction we are taking basic mathematics. Our goal is similar, to raise the standards of our students. In this case, so that they can compete globally. The I-Ching (Book of Changes) from which the symbol above comes, recognizes the dynamic balance of opposites, looks at the various means for change, and the acceptance that change is inevitable. See, the only thing missing is my tie!
2 Curriculum Demands Critical Thinking and Analysis Student/Student Interaction Student Preparedness The Tai Chi of Basic Persistence Time Management Student/Teacher Interaction Confidence Basis Arithmetic Problem Solving Teacher Preparedness Student Diversity Common Mathematical Core Evaluation Creating Student Growth Learning Environment
3 Looking at our students. The Tai Chi of Basic I always did poorly in math, so why bother studying. But I need this class for my major, and it s my third time. This stuff is too easy for me! I don t need to study. I m in the wrong class. Can I leave class early to study for Biology? Biology is a pre-med requirement.
4 Those students with math anxiety may find some success in returning to the fundamentals, but applications and making the connections is still difficult. Over-confident students have realized that they may not moving on. This student is in trouble.
5 Looking at the curriculum. The Tai Chi of Basic
6 Looking at a diverse population. The Tai Chi of Basic DRILL and PRACTICE Whether a students native language is English or not, many adapts to drill and practice. APPLICATIONS and READING For students whose language is NOT English, it is another hurdle. Native born students also have difficulty.
7 Looking at PERSISTENCE The Tai Chi of Basic MATH ANXIETY (w/excuse) ENCOURAGEMENT (Find a bone for the dog) HOPEFUL RESULT (Found a bone for the dog)
8 In most cases, there should not be a difference in what we say and what we do. I looked to Albert Einstein for his experience and intellect for what I should be teaching in my classroom. It is still a matter of choice, and I choose to believe the statement below.
9 In dealing with PROBLEM SOLVING, one has three areas to address. Create an environment for learning Promote discovery and long-term understanding The Tai Chi of Basic Support and Encourage Persistence
10 Creating an Environment for Learning
11
12 Addressing Isolation In each circle, write something that is important to you, and perhaps, you would like others to know about you.
13 Addressing Isolation In each circle, write something that is important to you, and perhaps, you would like others to know about you. FAMILY I have wife, Mary, who raises my two daughters, Barbara and Loretta, and my son, Jimmy.
14 Addressing Isolation In each circle, write something that is important to you, and perhaps, you would like others to know about you. FAMILY I have wife, Mary, who raises my two daughters, Barbara and Loretta, and my son, Jimmy. EDUCATION My parents never finished high school, and I am the oldest of 7 children, all of which except for one went to college and got a degree.
15 Addressing Isolation In each circle, write something that is important to you, and perhaps, you would like others to know about you. FAMILY I have wife, Mary, who raises my two daughters, Barbara and Loretta, and my son, Jimmy. MY JOB I love my job and mathematics. I am fortunate to be doing what I have been doing for 40 years. EDUCATION My parents never finished high school, and I am the oldest of 7 children, all of which except for one went to college and got a degree.
16 Addressing Isolation In each circle, write something that is important to you, and perhaps, you would like others to know about you. FAMILY I have wife, Mary, who raises my two daughters, Barbara and Loretta, and my son, Jimmy. MY JOB I love my job and mathematics. I am fortunate to be doing what I have been doing for 40 years. EDUCATION My parents never finished high school, and I am the oldest of 7 children, all of which except for one went to college and got a degree. Man Cave I m remodeling my home so that I can have a quiet place other than the garage.
17 Promote Discovery and Long-term Understanding
18 Challenge the Familiar Model mathematics and let their innate skills develop.
19 AND Embrace the Unfamiliar What is the initial value of the shaded region? A primary component of the Singapore Math course is the use of visual representations of mathematical quantities and its role in problem solving single and multi-step applications.
20 Extend to the Familiar Evaluating the expression when x = (3x 2). Solving the equation 2x = 6. What is the initial value of the shaded region?
21 PROBLEM SOLVING STARTS WITH BASIC MATHEMATICS
22 1. Understand the problem Paul and Cheryl are selling hats. Cheryl purchased two boxes of hats while Paul purchased three times as many. If 5/6 of Paul s purchase is 10 hats, how many hats did each of them purchase? 2. Devise a plan 3. Carry out the plan 4. Look back
23 1. Understand the problem Paul and Cheryl are selling hats. Cheryl purchased two boxes of hats while Paul purchased three times as many. If 5/6 of Paul s purchase is 10 hats, how many hats did each of them purchase? 2. Devise a plan 3. Carry out the plan 4. Look back
24 1. Understand the problem Paul and Cheryl are selling hats. Cheryl purchased two boxes of hats while Paul purchased three times as many. If 5/6 of Paul s purchase is 10 hats, how many hats did each of them purchase? 2. Devise a plan 3. Carry out the plan 4. Look back
25 1. Understand the problem Paul and Cheryl are selling hats. Cheryl purchased two boxes of hats while Paul purchased three times as many. If 5/6 of Paul s purchase is 10 hats, how many hats did each of them purchase? 2. Devise a plan 3. Carry out the plan 4. Look back Cheryl bought 4 hats and Paul purchased 12 hats. 5/6 of 12 is 10.
26 PROBLEM SOLVING Models Solutions Given the information below, what is the value of the shaded regions.
27 PROBLEM SOLVING (Words Models Solutions) Fred could not divide the amount of money in his pocket equally among his 4 kids. His wife gave him an additional $3 after which each of his 4 kids received $8.
28 PROBLEM SOLVING (Words Models Solutions) Fred could not divide the amount of money in his pocket equally among his 4 kids. His wife gave him an additional $3 after which each of his 4 kids received $8.
29 PROBLEM SOLVING (Words Models Solutions) Tristan divided a certain amount of money into 3 equal shares. He gave the first share to Betty, the second share to Veronica, and he then divided the remainder into 3 equal shares and gave one share to Archie. He kept the rest totaling $24. How much money did Tristan initially have?
30 PROBLEM SOLVING (Words Models Solutions) Tristan divided a certain amount of money into 3 equal shares. He gave the first share to Betty, the second share to Veronica, and he then divided the remainder into 3 equal shares and gave one share to Archie. He kept the rest totaling $24. How much money did Tristan initially have?
31 PROBLEM SOLVING and Linear Models Expression Given the model, create the algebraic expression. Illustration: What is the Algebraic Expression?
32 PROBLEM SOLVING and Linear Models Expression Given the model, create the algebraic expression. Illustration: What is the Algebraic Expression?
33 PROBLEM SOLVING and Linear Models Expression Given the model, create the algebraic expression. What is the Algebraic Expression?
34 PROBLEM SOLVING and Linear Models Expression Given the model, create the algebraic expression. What is the Algebraic Expression?
35 Linear Functions and the Order of Operations Model Given the algebraic expression, label the order of each operation involve in the process, and then create the model Operations
36 Linear Functions and the Order of Operations Model Given the algebraic expression, label the order of each operation involve in the process, and then create the model. Op 1 DIVISION Operations
37 Linear Functions and the Order of Operations Model Given the algebraic expression, label the order of each operation involve in the process, and then create the model. Op 1 DIVISION Op 2 SUM 3 Operations
38 Linear Functions and the Order of Operations Model Given the algebraic expression, label the order of each operation involve in the process, and then create the model. Op 1 DIVISION Op 2 SUM 3 Operations Op 3 TIMES
39 Linear Functions and the Order of Operations Model Given the algebraic expression, label the order of each operation involve in the process, and then create the model Operations
40 Linear Functions and the Order of Operations Model Given the algebraic expression, label the order of each operation involve in the process, and then create the model. Op 1 DIVIDE Operations
41 Linear Functions and the Order of Operations Model Given the algebraic expression, label the order of each operation involve in the process, and then create the model. Op 1 DIVIDE Op 2 SUM Operations
42 Linear Functions and the Order of Operations Model Given the algebraic expression, label the order of each operation involve in the process, and then create the model. Op 1 DIVIDE Op 2 SUM Op 3 TIMES Operations
43 Linear Functions and the Order of Operations Model Given the algebraic expression, label the order of each operation involve in the process, and then create the model. Op 1 DIVIDE Op 2 SUM Op 3 TIMES Op 4 SUM Operations
44 Linear Functions and the Order of Operations Model Given the algebraic expression, label the order of each operation involve in the process, and then create the model. Op 1 DIVIDE Op 2 SUM Op 3 TIMES Op 4 SUM Op 5 DIVIDE Operations
45 PROBLEM SOLVING: Evaluating an Expression. Given the model and the corresponding input value, determine the value the expression. If the value of the x is 90, determine the value of the expression
46 PROBLEM SOLVING: Evaluating an Expression. Given the model and the corresponding input value, determine the value the expression. If the value of the x is 7, determine the value of the expression. Illustration:
47 PROBLEM SOLVING: Evaluating an Expression. Given the model and the corresponding input value, determine the value the expression. If the value of the x is 7, determine the value of the expression. Illustration:
48 PROBLEM SOLVING Models Solving an Equation Given the model and value of the expression, determine the value of its input. The expression has a value of 25; so what is the value of x?
49 PROBLEM SOLVING Models Solving an Equation Given the model and value of the expression, determine the value of its input. 28 The expression has a value of 25; so what is the value of x?
50 PROBLEM SOLVING Models Solving an Equation Given the model and value of the expression, determine the value of its input. Illustration: The expression has a value of 8; so what is the value of x? 4 4
51 PROBLEM SOLVING Models Solving an Equation Given the model and value of the expression, determine the value of its input. Illustration: The expression has a value of 8; so what is the value of x? 4 4 4
52 PROBLEM SOLVING Models Solving an Equation Given the model and value of the expression, determine the value of its input. Illustration: The expression has a value of 8; so what is the value of x?
53 PROBLEM SOLVING Models Solving an Equation Given the model and value of the expression, determine the value of its input. Illustration: The expression has a value of 8; so what is the value of x?
54 PROBLEM SOLVING Models Solving an Equation Given the model and value of the expression, determine the value of its input. Illustration: The expression has a 27 value of 8; so what is the value of x?
55 PROBLEM SOLVING Models Solving an Equation via the Algebraic Method Given the model and value of the expression, determine the value of its input. 1) ADD 2 to get 8 for the YELLOW box Describe the steps you will need to do to solve for x.
56 PROBLEM SOLVING Models Solving an Equation via the Algebraic Method Given the model and value of the expression, determine the value of its input. 2) MULTIPLY by 3 to get Describe the steps you will need to do to solve for x.
57 PROBLEM SOLVING Models Solving an Equation via the Algebraic Method Given the model and value of the expression, determine the value of its input. 3) ADD 1 to get Describe the steps you will need to do to solve for x.
58 PROBLEM SOLVING Models Solving an Equation via the Algebraic Method Given the model and value of the expression, determine the value of its input. 4) DIVIDE by 5 to get Describe the steps you will need to do to solve for x.
59 PROBLEM SOLVING Models Solving an Equation via the Algebraic Method Given the model and value of the expression, determine the value of its input ) Subtract 5 from 13 to get the length of the left rectangle.
60 PROBLEM SOLVING Models Solving an Equation via the Algebraic Method Given the model and value of the expression, determine the value of its input ) Divide by 2 8
61 PROBLEM SOLVING Models Solving an Equation via the Algebraic Method Given the model and value of the expression, determine the value of its input ) Add 3 8
62 An Important Goal: Problem Solving and Critical Thinking w/ Applications
63 Application Problem #1 out of 10 The Tai Chi of Basic Jim took $23.00 with him to go shopping. His sister, Loretta took $13.00 more than he did. How much did Loretta take shopping?
64 Application Problem #2 out of 10 The Tai Chi of Basic Judy bought some eggs. She used 2/5 of the eggs to bake cakes. She had 18 eggs left. How many eggs did she did she buy?
65 Application Problem #3 out of 10 The Tai Chi of Basic Tomas took a certain amount of money from his bank account to go shopping at the mall. He spent 2/5 of the money on clothing, and 2/3 of the remainder for power tools. What fraction of his original amount was left? What fraction of his original amount was left?
66 Application Problem #4 out of 10 The Tai Chi of Basic Tom spent three-quarters of his money on a dictionary. He spent one-half of the remainder on a calculator. The dictionary cost $30 more than the calculator. How much does the dictionary cost? dictionary cost $30 more.
67 Application Problem #5 out of 10 The Tai Chi of Basic There are 20 workers in the library. 55% of them were males. How many fewer females than males worked in the library? 100% 100% % 100% 10% more males than females employed 10%
68 Application Problem #6 out of 10 The Tai Chi of Basic Mary determined that the population of monarch butterflies at a particular site was 12,000. She estimated that next year there would be a 6% increase each year. What would be the estimated population of monarch butterflies next year?
69 Application Problem #7 out of 10 The Tai Chi of Basic A shopkeeper had 4 handbags which were of the same cost price. He sold 3 of them at 40% more than the cost price. He sold the fourth handbag at cost price. He received a total of $260 altogether. Find the cost price of each handbag. 520% $ % 100%
70 Application Problem #8 out of 10 The Tai Chi of Basic Sally is given $5 more allowance than Megan each week. They each spend $12 per week and save the rest. When Sally has saved $60, Megan saved $20. Sally Megan Sally savings savings $5 $60 Find out Sally s allowance. Megan $40 8 weeks of savings from both Sally and Megan
71 Application Problem #9 out of 10 The Tai Chi of Basic In a class, at the beginning of the semester, the ratio of girls to boys is 5:3. If an additional 4 girls and 12 boys enrolled, there would be the same number of girls as boys in the class. How many girls were there at the beginning of the semester? Initially, girls boys 4 additional girls 12 additional boys
72 Application Problem #10 out of 10 The Tai Chi of Basic Ali had $130 and his brother had $45. When their mother gave each of them an equal amount of money, Ali had twice as much as his brother. How much did their mother contribute to each of them?
73 Support and Encourage Persistence
74 Solved it and ready to do the next one. Okay, ready to begin this problem. The vicious elliptical path problem solving... P E R S I S T E N C E It s tougher than I thought! My group mates think that we can get together in the quad to work on it. Hey, maybe someone in my class study group can help me? I ve read it over 25 times. Nothing. I remember now why I hate math.
75 ComboReview The Tai Chi of Basic Half of a Combo-Review (part 1) is taken home giving many students to develop work groups. In class, part 2 with similar objects is given. A master form where answers are recorded when the groups get together is turned in for credit. Everybody works, everybody benefits.
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